The constants for Antoine’s equation for TCE (based on log10 and ˚C) are: A=
6.5183, B = 1018.6 and C = 192.7. If a container (negligible volume) is placed in a
sealed room 1000 m3 at 30 ˚C, how many grams of TCE will evaporate upon reaching
equilibrium with the liquid and what is the TCE concentration in the room? If the
temperature in the room is lowered to 10 ˚C, how much TCE will condense and what
will be the resulting air concentration?
To solve this problem, we will use Antoine's equation to calculate the vapor pressure of TCE at the given temperatures. We can then use the ideal gas law and the volume of the room to calculate the amount of TCE that evaporates or condenses.
1. Calculate the vapor pressure of TCE at 30°C:
The vapor pressure (P) can be calculated using Antoine's equation:
log10(P) = A - (B / (C + T)), where T is the temperature in ˚C.
Plugging in the values: A = 6.5183, B = 1018.6, C = 192.7, and T = 30°C:
log10(P) = 6.5183 - (1018.6 / (192.7 + 30))
Solve for log10(P) and then convert it back to P using 10^(log10(P)).
2. Calculate the amount of TCE that evaporates:
The amount of TCE (in moles) that evaporates can be calculated using the ideal gas law:
PV = nRT, where P is the vapor pressure, V is the volume, n is the amount in moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Rearranging the equation: n = PV / RT.
Convert the volume from cubic meters to liters (1000 m^3 = 1000000 L) and convert the temperature from ˚C to Kelvin (T = 30 + 273.15).
Calculate the number of moles using the obtained vapor pressure and the volume:
n = (P * V) / (R * T).
Given that the molar mass of TCE is 131.4 g/mol, we can find the mass of TCE that evaporates:
Mass = n * molar mass.
3. Calculate the TCE concentration in the room:
The concentration (in ppm) can be calculated as the mass of TCE evaporated divided by the volume of the room, all multiplied by 1,000,000 to convert it to ppm:
Concentration = (mass / V) * 1,000,000.
4. Calculate the amount of TCE that condenses at 10˚C:
Repeat steps 1 and 2 using the temperature of 10°C instead of 30°C to calculate the vapor pressure and the amount of TCE that evaporates at that temperature.
5. Calculate the resulting air concentration:
Repeat step 3 using the mass of TCE that condenses and the volume of the room to calculate the resulting air concentration.
By following these steps, you should be able to find the answer to your question.